A 3-DIMENSIONAL ANALYSIS OF ANISOTROPIC INHOMOGENEOUS AND LAMINATED PLATES

An asymptotic theory for bending and stretching of anisotropic inhomog eneous and laminated plates is developed based on the three-dimensiona l elasticity without apriori assumptions. The inhomogeneities are cons idered to vary through the plate thickness, and laminated plates belon g to an important class of this inhomogeneous plate. Through appropria te nondimensionalization of the basic equations and expansion of the d isplacements and stresses in powers of a small parameter, we obtain se ts of differential equations of various orders, that can be integrated successively to determine the three-dimensional solutions for the ani sotropic inhomogeneous plate under lateral tractions and edge loads. W e show that the governing equations for the asymptotic solutions are p recisely those in the classical laminated plate theory (CLT) with nonh omogeneous terms. As a result, all the displacement and stress compone nts can be determined in a systematic way, using the same solution met hod as that for the CLT solution. While the solution is no more diffic ult than the CLT, the asymptotic solution converges rapidly and gives accurate results. The basic theory and the solution approach are illus trated by considering a problem of symmetric laminated plates under th e action of edge loads, and Pagano's problem of a bi-directional lamin ated plate under lateral transverse loads. Elasticity solutions for th e problems are obtained in a simple manner, without treating the indiv idual layers and considering the interfacial continuity conditions in particular.